{"id":"https://openalex.org/W2057974767","doi":"https://doi.org/10.1145/1217856.1217860","title":"An approximation scheme for stochastic linear programming and its application to stochastic integer programs","display_name":"An approximation scheme for stochastic linear programming and its application to stochastic integer programs","publication_year":2006,"publication_date":"2006-11-01","ids":{"openalex":"https://openalex.org/W2057974767","doi":"https://doi.org/10.1145/1217856.1217860","mag":"2057974767"},"language":"en","primary_location":{"id":"doi:10.1145/1217856.1217860","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1217856.1217860","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030030349","display_name":"David B. Shmoys","orcid":"https://orcid.org/0000-0003-3882-901X"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David B. Shmoys","raw_affiliation_strings":["Cornell University, Ithaca, New York","Cornell University Ithaca,, New York"],"affiliations":[{"raw_affiliation_string":"Cornell University, Ithaca, New York","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Cornell University Ithaca,, New York","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031968426","display_name":"Chaitanya Swamy","orcid":"https://orcid.org/0000-0003-1108-7941"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Chaitanya Swamy","raw_affiliation_strings":["University of Waterloo, Waterloo, Ontario, Canada","University of Waterloo, Waterloo, Ontario, CANADA"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of Waterloo, Waterloo, Ontario, CANADA","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030030349"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":7.4298,"has_fulltext":false,"cited_by_count":111,"citation_normalized_percentile":{"value":0.97122411,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"53","issue":"6","first_page":"978","last_page":"1012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.7078162431716919},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.6728896498680115},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.6606390476226807},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6240212321281433},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5204620361328125},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.51361083984375},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5107738971710205},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.48033419251441956},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.45502692461013794},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.45035654306411743},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.42374444007873535},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3465244770050049}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.7078162431716919},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.6728896498680115},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.6606390476226807},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6240212321281433},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5204620361328125},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.51361083984375},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5107738971710205},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.48033419251441956},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.45502692461013794},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.45035654306411743},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.42374444007873535},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3465244770050049},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1217856.1217860","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1217856.1217860","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.115.8157","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.8157","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uwaterloo.ca/~cswamy/papers/stochopt.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.89.3213","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.3213","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ist.caltech.edu/~cswamy/papers/stochopt.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.89.3237","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.3237","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.orie.cornell.edu/~shmoys/ShmoysSwamy05-journal.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W182881619","https://openalex.org/W347166089","https://openalex.org/W569789896","https://openalex.org/W586693846","https://openalex.org/W1484951415","https://openalex.org/W1490324987","https://openalex.org/W1560324410","https://openalex.org/W1569990960","https://openalex.org/W1696776098","https://openalex.org/W1752958389","https://openalex.org/W1973529814","https://openalex.org/W1976432206","https://openalex.org/W1980412153","https://openalex.org/W1981673685","https://openalex.org/W1983916623","https://openalex.org/W2000257769","https://openalex.org/W2002285507","https://openalex.org/W2019062750","https://openalex.org/W2058681351","https://openalex.org/W2076746184","https://openalex.org/W2100440346","https://openalex.org/W2109156431","https://openalex.org/W2109533535","https://openalex.org/W2112058494","https://openalex.org/W2116509768","https://openalex.org/W2117399775","https://openalex.org/W2139841919","https://openalex.org/W2140844111","https://openalex.org/W2142092335","https://openalex.org/W2143863355","https://openalex.org/W2157054705","https://openalex.org/W2165775468","https://openalex.org/W2502170570","https://openalex.org/W2809211406","https://openalex.org/W3125256586","https://openalex.org/W3148765228","https://openalex.org/W4302155765"],"related_works":["https://openalex.org/W2056597184","https://openalex.org/W1712180277","https://openalex.org/W1608414128","https://openalex.org/W2543175834","https://openalex.org/W2029933769","https://openalex.org/W2551034790","https://openalex.org/W2096382750","https://openalex.org/W2094388041","https://openalex.org/W2377757044","https://openalex.org/W3102280101"],"abstract_inverted_index":{"Stochastic":[0],"optimization":[1,136],"problems":[2,137],"attempt":[3],"to":[4,55],"model":[5],"uncertainty":[6],"in":[7,84,87,107,157],"the":[8,13,23,39,49,56,90,93,105,110,128,139,155,158,187,191,201],"data":[9,40,51,142],"by":[10,17,145],"assuming":[11],"that":[12,66,112,169],"input":[14],"is":[15,52,143],"specified":[16],"a":[18,68,96,101,122,146,174,179],"probability":[19],"distribution.":[20],"We":[21,64],"consider":[22,196],"well-studied":[24],"paradigm":[25],"of":[26,71,92,98,104,109,193,200],"2-stage":[27,72,133],"models":[28,74],"with":[29,75,121,178],"recourse:":[30],"first,":[31],"given":[32,144],"only":[33],"distributional":[34],"information":[35],"about":[36],"(some":[37],"of)":[38],"one":[41,77],"commits":[42],"on":[43,154],"initial":[44],"actions,":[45],"and":[46,89,149,208],"then":[47],"once":[48],"actual":[50],"realized":[53],"(according":[54],"distribution),":[57],"further":[58],"(recourse)":[59],"actions":[60],"can":[61],"be":[62],"taken.":[63],"show":[65],"for":[67,79,132,164,173,186],"broad":[69],"class":[70],"linear":[73],"recourse,":[76],"can,":[78],"any":[80],"\u03f5":[81],">":[82],"0,":[83],"time":[85],"polynomial":[86],"1/\u03f5":[88],"size":[91],"input,":[94],"compute":[95],"solution":[97],"value":[99],"within":[100],"factor":[102],"(1+\u03f5)":[103],"optimum,":[106],"spite":[108],"fact":[111],"exponentially":[113],"many":[114],"second-stage":[115],"scenarios":[116],"may":[117],"occur.":[118],"In":[119],"conjunction":[120],"suitable":[123],"rounding":[124,162],"scheme,":[125],"this":[126],"yields":[127],"first":[129],"approximation":[130,171],"algorithms":[131],"stochastic":[134,165,188,198],"integer":[135,166],"where":[138],"underlying":[140],"random":[141],"\u201cblack":[147],"box\u201d":[148],"no":[150],"restrictions":[151],"are":[152,197],"placed":[153],"costs":[156],"two":[159],"stages.":[160],"Our":[161],"approach":[163],"programs":[167],"shows":[168],"an":[170],"algorithm":[172],"deterministic":[175],"analogue":[176],"yields,":[177],"small":[180],"constant-factor":[181],"loss,":[182],"provably":[183],"near-optimal":[184],"solutions":[185],"generalization.":[189],"Among":[190],"range":[192],"applications,":[194],"we":[195],"versions":[199],"multicommodity":[202],"flow,":[203],"set":[204],"cover,":[205,207],"vertex":[206],"facility":[209],"location":[210],"problems.":[211]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}